You may already know that this route will take you through some of the least populated areas of France. So my suggestion would be to ask ahead, as Roland49 just mentioned, at the auberges or gîtes where you stay. By that I mean, where to dine on the next segments of the GR65.
I think your best bets will be in the larger towns: Estaing, Conques, Figeac, Cahors, etc. With perhaps one exception - tiny Aubrac. There you'll find fabulous pastries at Chez Germaine as well as good food and charming dining ambience at L’hôtel la Dômerie. (My experiences at these Aubrac establishments is almost 10 years old, so check ahead, again as Roland 49 advised.)
An anecdote: on my second trip across the Aubrac Plateau I was with my wife and we were overtaken by a solo-walking Frenchman. We chatted for a few minutes. He told us that there was a very good tête de veau served at the hotel in Aubrac. And, did we know, a good tête de veau was the favorite dish of Jacques Chirac, the former French President. And that this is not a dish we should sample in an average restaurant.
Quite informative was the Frenchman, providing à la fois a restaurant recommendation, a suggested dish and also a bit of lore about it. But it also was an example of what we later learned was the French enthusiasm for forward feeding, the good fromage in this department, the beef in another, and the arrival in foie gras territory. Same for spirits: the wine of Cahors, then the territory of Armagnac. The list goes on and on.
So we decided to follow the Frenchman's advice and treated ourselves to a charming, modestly priced room (again, nearly ten years ago). A bath and a nap had us ready for dinner. The small dining room was nicely appointed. My wife admired the burnished wooden mantle above the room's fireplace. And the Frenchman was already seated. With a companion. His wife? A fellow hiker? Their table was thirty feet from ours, on the opposite side of the dining room. From that distance we couldn't determine whether he was, indeed, tucking into Jacques Chirac's favorite dish. But, amazingly, we could hear, muffled and low, their conversation. Despite people seated at a table between ours and the Frenchman's.
I am an adventurous eater, but I didn't opt for the tête de veau of Aubrac. I would do that with the French hiking group we would later join. But that day an encounter with a random Frenchman led us to a charming small hotel. And, more importantly, to insights about French culture: the importance ascribed to food and drink, and how it is possible to carry on a conversation in a lowered voice. A lot of education in one day.